When an image of a scene is sampled (e.g. during capture of the image at the sensor in a digital camera), aliasing will occur in the captured image if the density of samples is not sufficiently high. The density of the samples is determined by the configuration of the sensor and the lens system of the camera and describes a resolution to which the image of the scene may be captured. Aliasing occurs when the image being sampled contains frequencies that are higher than the Nyquist limit 1/(2d) where d represents spacing between samples. Aliasing may be removed by optically low-pass filtering the image at capture to remove the frequencies susceptible to aliasing. Unfortunately, as low-pass filtering blurs the image, camera optics are typically designed such that images are slightly under-sampled to improve the apparent sharpness of the sampled image. This applies also to computer generated images where similar sharpness is desirable. Many methods of rendering computer graphics also introduce aliasing.
Small amounts of aliasing are not usually detected when viewing the captured image. However, when an image is resampled at a higher resolution, the aliasing in the original image is magnified and becomes much more visible in the higher resolution image. Artefacts caused by aliasing are especially visible along edges in the image data, where they are sometimes referred to as “jaggies”. Such artefacts are a significant cause of quality degradation in up-scaled images.
Increasing the resolution of an image is generally performed using an interpolation process to generate pixels of the higher resolution image from pixels of the input image. Many methods based on modifying the interpolation process in the presence of edge shave been proposed to deal with problems due to aliasing. For example the resulting sharpness produced by an interpolating kernel may be varied in edge regions or a kernel may be selected that is modified or oriented to match the orientation of an edge. In some techniques, pixel patterns are matched to dictionaries that provide specific interpolation rules to generate the missing output sample. Machine learning methods have also been proposed as a means of generating the interpolation rules while others use hand coded rules. Many of these methods suffer from the fact that edge orientations are quantized which creates visible artefacts at the boundaries between regions where different kernels have been applied. Other methods are constrained because their rules can only be applied to fixed rate interpolation. All methods based on modifying the interpolation process suffer from unpredictable artefacts that are a result of their empirical or arbitrary construction. To prevent such artefacts it is necessary to moderate the use of the techniques, often via separate sets of rules which add further unpredictability and complexity and may actually degrade image quality in certain circumstances.
More theoretical methods that optimise the kernel selection according to the data have been proposed but these are typically iterative techniques that remain too complex to implement in hardware for consumer electronics.
It is the aim of almost all adaptive interpolation algorithms to remove aliased frequencies, as they are the cause of jagged artefacts. However, by removing aliased frequencies, the edges of the resultant image are blurred. To produce the sharpest upsampled image, the aliased frequencies should be recovered, rather than removed.
There is, therefore, a need for an efficient interpolation method that is able to restore aliased frequencies, without introducing additional artefacts.